Abstract A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let Γ {\varGamma} be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of Γ {\varGamma} . In the case where G acts transitively on the edge set and quasiprimitively on the vertex set of Γ {\varGamma} , we prove that either G is almost simple, or G is a primitive group of affine type. If further G is an almost simple primitive group, then, with two exceptions, the socle of G acts transitively on the edge set of Γ {\varGamma} .

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关于奇数阶双素价的拟本原边传递图

摘要 如果一个图的自同构群在边集上可传递地作用，则该图是边传递的。在本文中，我们研究了奇数阶和双素价的边传递图的自同构群。设 Γ {\varGamma} 是一个奇数阶和两倍素价的连通图，让 G 是 Γ {\varGamma} 的自同构群的一个子群。在 G 在边集上传递作用并在 Γ {\varGamma} 的顶点集上拟本原作用的情况下，我们证明要么 G 几乎是简单的，要么 G 是仿射类型的本原群。如果进一步的 G 是一个几乎简单的原始群，那么，除了两个例外，G 的 socle 传递地作用于 Γ {\varGamma} 的边集。